This Study Tests the New Medicine BI 754111 Alone or in Combination With Another New Substance BI 754091 in Patients With Advanced Cancer. The Study Tests Different Doses to Find the Best Dose for Continuous Treatment.

Inclusion Criteria: * Provision of signed and dated, written Informed consent form (ICF) prior to any trial-specific procedures, sampling, or analyses * Patients ≥18 years of age at the time of signature of the ICF * Part I (dose escalation): --Patients with a confirmed diagnosis of advanced, unresectable, and/or metastatic solid tumours (any type) * For whom no therapy of proven efficacy exists, or who are not amenable to standard therapies. * Must have measurable lesions according to Response Evaluation Criteria in Solid Tumours (RECIST) v1.1 * Previous treatment with an anti-programmed cell death 1 (receptor) (PD-1) monoclonal antibody (mAb) is allowed as long as the last administration of the anti-PD-1 mAb on the previous treatment is a minimum of 60 days prior to starting treatment in this trial. * Part II (dose expansion): * Patients must have measurable disease per RECIST v1.1 criteria, must have at least 1 tumour lesion amenable to biopsy, and must be medically fit and willing to undergo a biopsy before first treatment (if adequate archival tissue is not available) and, unless clinically contraindicated, after 6 weeks on therapy. * Dose Expansion Cohorts: Patients with a confirmed diagnosis of advanced, unresectable, and/or metastatic solid tumours of one of the following types: * Second and 3rd line Non-small cell lung cancer (NSCLC) patients: * Must have progressed on anti-PD-1 or anti-programmed cell death ligand 1 (PD-L1) treatment after having achieved radiologically confirmed benefit (minimum of stable disease) * Must have had a minimum duration of benefit of 4 months and minimum treatment duration of 2 months on the previous anti- PD-1 or anti-PD-L1 treatment without experiencing disease progression during that period. * The anti-PD-1- or anti-PD-L1-containing treatment must have been the latest treatment regimen prior to enrolling in this trial * Must be within \>4 and \<12 weeks since the latest treatment and their first dose in this trial. Patients who have had anti-PD-1 or anti-PD-L1 monotherapy as their first-line NSCLC treatment regimen must have a PD-L1 expression level of ≥1% at baseline (local validated testing). * Anti-PD-1 or anti-PD-L1 treatment-naïve patients with microsatellite stable Metastatic colorectal Cancer (mCRC): * Patients must have had ≥ 1 line treatment * Must have microsatellite stable disease (identified using any validated test) * Must be anti-PD-1 and anti-PD-L1 treatment naïve * Anti-PD-1 or anti-PD-L1 pretreated patients with any high Tumour mutational burden (TMB) (≥10 mutations/Mb) and/or Microsatellite instability high (MSI-H) and/or DNA MMRd solid tumours * Patients must have high TMB (≥ 10 mutations/Mb) and/or MSI-H and/or DNA mismatch repair deficient (MMRd) (measured using any validated test). * Patients must have received 1 prior anti-PD-1 or anti-PD-L1 treatment regimen. * 1st-line squamous or non-squamous NSCLC patients: * Patients must be treatment naïve * Must be epidermal growth factor receptor (EGFR) and anaplastic lymphoma kinase (ALK) wild type (only applicable to patients with non-squamous NSCLC) * Regardless of PD-L1 expression level. However, the number of patients with high level of PD-L1 expression (≥50% PD-L1) will be limited to a maximum of 10 patients * Eastern Cooperative Oncology Group (ECOG, R01-0787) score: 0 to 1 * Life expectancy of at least 12 weeks after the start of the treatment according to the Investigator's judgement * Male or female patients. Women of childbearing potential (WOCBP) and men able to father a child must be ready and able to use highly effective methods of birth control (that result in a low failure rate of less than 1% per year when used consistently and correctly) during trial participation and for at least 6 months after the last administration of trial medication. A list of contraception methods meeting these criteria is provided in the patient information. Exclusion Criteria: * Major surgery (major according to the Investigator's assessment) performed within 12 weeks prior to first trial treatment or planned within 12 months after screening, e.g., hip replacement * Patients who must or wish to continue the intake of restricted medications (see Section 4.2.2.2) or any drug considered likely to interfere with the safe conduct of the trial * Previous enrolment in this trial * Any investigational or anti-tumour treatment, except BI 754091, within 4 weeks or within 5 half-life periods (whichever is shorter) prior to the initiation of trial treatment. * Any unresolved toxicities from prior therapy greater than CTCAE Grade 1 at the time of starting study treatment with the exception of alopecia and Grade 2 neuropathy due to prior platinum-based therapy * Prior treatment with anti-Lymphocyte-activation gene 3 (LAG-3) agents * Patients with NSCLC that has EGFR mutations or ALK rearrangements (only applicable to patients with non-squamous NSCLC). * Presence of other active invasive cancers other than the one treated in this trial within 5 years prior to screening, with the exception of appropriately treated basal-cell carcinoma of the skin, in situ carcinoma of the uterine cervix, or other local tumours considered cured by local treatment * Untreated brain metastasis(es) that may be considered active. Patients with previously treated brain metastases may participate provided they are stable (i.e., without evidence of PD by imaging for at least 4 weeks prior to the first dose of trial treatment, and any neurologic symptoms have returned to baseline), and there is no evidence of new or enlarging brain metastases. * Inadequate organ function or bone marrow reserve as demonstrated by the laboratory values presented in Table 3.3.3: 1. * Any of the following cardiac criteria: * Mean resting corrected QT interval (QTc) \>470 msec * Any clinically important abnormalities (as assessed by the Investigator) in rhythm, conduction, or morphology of resting ECGs, e.g., complete left bundle branch block, third degree heart block * Any factors that increase the risk of QTc prolongation or risk of arrhythmic events such as heart failure, hypokalaemia, congenital long QT syndrome, family history of long QT syndrome or unexplained sudden death under 40 years-of-age, or any concomitant medication known to prolong the QT interval * Patients with an ejection fraction (EF) \<55% or the lower limit of normal of the institutional standard will be excluded. Only in cases where the Investigator (or the treating physician or both) suspects cardiac disease with negative effect on the EF, will the EF be measured during screening using an appropriate method according to local standards to confirm eligibility (e.g., echocardiogram, multi-gated acquisition scan). A historic measurement of EF no older than 6 months prior to first administration of study drug can be accepted provided that there is clinical evidence that the EF value has not worsened since this measurement in the opinion of the Investigator or of the treating physician or both. * History of pneumonitis within the last 5 years * History of severe hypersensitivity reactions to other mAbs * Immunosuppressive corticosteroid doses (\>10 mg prednisone daily or equivalent) within 4 weeks prior to the first dose of study treatment. * Active autoimmune disease or a documented history of autoimmune disease, except vitiligo or resolved childhood asthma/atopy * Active infection requiring systemic treatment (antibacterial, antiviral, or antifungal therapy) at start of treatment in this trial * Known history of human immunodeficiency virus infection or an active hepatitis B or C virus infection * Interstitial lung disease * Chronic alcohol or drug abuse or any condition that, in the Investigator's opinion, makes him/her an unreliable trial subject, unlikely to complete the trial, or unable to comply with the protocol procedures.